On the structure of nearly pseudo-Kähler manifolds
Copyright policy )On the structure of nearly pseudo-Kähler manifolds
Firstly we give a condition to split off the K"ahler factor from a nearly pseudo-K"ahler manifold and apply this to get a structure result in dimension 8. Secondly we extend the construction of nearly K"ahler manifolds from twistor spaces to negatively curved quaternionic K"ahler manifolds and para-quaternionic K"ahler manifolds. The class of nearly pseudo-K"ahler manifolds obtained from this construction is characterized by a holonomic condition. The combination of these results enables us to give a classification result in (real) dimension 10. Moreover, we show that a strict nearly pseudo-K"ahler six-manifold is Einstein.
to appear in Monatshefte f"ur Mathematik
- University of Hannover Germany
Issues of holonomy in differential geometry, Mathematics - Differential Geometry, Twistor methods in differential geometry, pseudo-Riemannian metrics, twistor space, 53C25, 53C15, 53C26, 53C29, 53C28, Differential Geometry (math.DG), 53C15; 53C28; 53C29; 53C25; 53C26, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, nearly Kähler manifolds
Issues of holonomy in differential geometry, Mathematics - Differential Geometry, Twistor methods in differential geometry, pseudo-Riemannian metrics, twistor space, 53C25, 53C15, 53C26, 53C29, 53C28, Differential Geometry (math.DG), 53C15; 53C28; 53C29; 53C25; 53C26, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, nearly Kähler manifolds
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